The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

An analysis of elementary school teachers' mindset regarding students' mathematical ability

학생의 수학적 능력에 대한 초등학교 교사의 마인드셋 분석

  • Received : 2024.07.04
  • Accepted : 2024.08.08
  • Published : 2024.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to analyze elementary school teachers' mindsets about students' mathematical ability. For this purpose, we developed a 20-item scale to measure teachers' mindset through a review of the literature. In order to verify the developed scale, a survey was conducted among 158 elementary school teachers, and the structure of the items was analyzed by exploratory factor analysis. As a result, three factors were identified: "growth mindset toward change in mathematical ability", "fixed mindset toward change in mathematical ability", and "mindset toward innate mathematical ability". Four groups were distinguished by latent profile analysis, using the scores on these three factors as variables, to characterize the different groups of teachers based on their mindset. The groups with the most participants in the study were, in order, growth mindset teachers, neutral mindset teachers, strong growth mindset teachers, and fixed mindset teachers. Interviews were also conducted with representative participants from each group to learn more about the characteristics of teachers in each profile. Based on the results of the study, we discussed the implications of mindset in terms of the classification of teachers' mindset about students' mathematical ability, the popularity of growth mindset among elementary school teachers in Korea, and research on teachers' mindset about innate mathematical ability.

본 연구의 목적은 학생의 수학적 능력에 대한 초등학교 교사의 마인드셋을 분석하는 것이다. 이를 위해 선행연구를 고찰하여 학생의 수학적 능력에 초점을 두고 교사의 마인드셋을 측정하기 위한 20개의 문항으로 구성된 검사 도구를 개발하였다. 개발된 검사 도구를 검증하기 위하여 초등학교 교사 158명을 대상으로 설문조사를 실시하고, 이를 활용한 탐색적 요인 분석을 통해 문항의 구조를 분석하였다. 그 결과 '수학적 능력의 변화에 대한 성장 마인드셋', '수학적 능력의 변화에 대한 고정 마인드셋', '타고난 수학적 능력에 대한 마인드셋'이라는 세 가지 요인이 발견되었다. 이 세 가지 요인별 점수를 변수로 설정하여 마인드셋에 따른 교사 집단별 특징을 알아보기 위해 잠재프로파일 분석을 시행하였다. 그 결과, 네 개의 집단이 도출되었다. 가장 많은 연구 참여자가 속한 집단은 '성장 마인드셋을 지닌 교사'이고 다음으로 '중립 마인드셋을 지닌 교사'가 많았다. '강한 성장 마인드셋을 지닌 교사'와 '고정 마인드셋을 지닌 교사'가 뒤를 이었다. 각 프로파일에 속한 교사의 특징을 자세히 알아보기 위해 선정된 교사와 면담을 진행하여 해당 교사의 응답 결과를 탐색하였다. 이를 바탕으로 학생의 수학적 능력에 대한 교사의 마인드셋의 분류, 우리나라 초등학교 교사의 성장 마인드셋의 경향, 타고난 수학적 능력에 대한 교사의 마인드셋 연구 등의 측면에서 마인드셋에 대한 시사점을 논의하였다.

Keywords

References

  1. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332. https://doi.org/10.1007/BF02294359 
  2. Berlin, K. S., Williams, N. A., & Parra, G. R. (2014). An introduction to latent variable mixture modeling (part 1): Overview and cross-sectional latent class and latent profile analyses. Journal of Pediatric Psychology, 39(2), 174-187. https://doi.org/10.1093/jpepsy/jst084 
  3. Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246-263. https://doi.org/10.1111/j.1467-8624.2007.00995.x 
  4. Boaler, J. (2019). Limitless mind: Learn, lead, and live without barriers. HarperCollins. 
  5. Boaler, J. (2022). Mathematical mindsets: Unleashing students' potential through creative mathematics, inspiring messages and innovative teaching. John Wiley & Sons. 
  6. Bostwick, K. C., Collie, R. J., Martin, A. J., & Durksen, T. L. (2020). Teacher, classroom, and student growth orientation in mathematics: A multilevel examination of growth goals, growth mindset, engagement, and achievement. Teaching and Teacher Education, 94, 103100. https://doi.org/10.1016/j.tate.2020.103100 
  7. Celeux, G., & Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13, 195-212. https://doi.org/10.1007/BF01246098 
  8. Chestnut, E. K., Lei, R. F., Leslie, S. J., & Cimpian, A. (2018). The myth that only brilliant people are good at math and its implications for diversity. Education Sciences, 8(2), 65. https://doi.org/10.3390/educsci8020065 
  9. Clark, S. L. (2010). Mixture* modeling with behavioral data [Doctoral dissertation, University of California, Los Angeles]. 
  10. Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10(1), 7. https://doi.org/10.7275/jyj1-4868 
  11. Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Psychology Press.
  12. Dweck, C. S. (2006). Mindset: The new psychology of success. Random House. 
  13. Dweck, C. S., & Leggett, E. L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95(2), 256-273. https://doi.org/10.1037/0033-295X.95.2.256 
  14. Fabrigar, L. R., & Wegener, D. T. (2011). Exploratory factor analysis. Oxford University Press.
  15. Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage. 
  16. Gutshall, C. A. (2013). Teachers' mindsets for students with and without disabilities. Psychology in the Schools, 50(10), 1073-1083. https://doi.org/10.1002/pits.21725 
  17. Heo, H. J., & Kim, S. M. (2022). A study on the beliefs of primary and secondary pre-teachers with a focus on math mindset. Journal of Learner-Centered Curriculum and Instruction, 22(15), 765-779. https://doi.org/10.22251/jlc-ci.2022.22.15.765 
  18. Hwang, J. H., Tak, B. J., Lee, S. E., Kim, H. M., & Lee, H. Y. (2022). Realationships among students' attitude toward mathematics, mindset, and teachers' mindset. School Mathematics, 24(4), 525-549. https://doi.org/10.57090/sm.2022.12.24.4.525 
  19. Infurna, F. J., & Grimm, K. J. (2018). The use of growth mixture modeling for studying resilience to major life stressors in adulthood and old age: Lessons for class size and identification and model selection. The Journals of Gerontology: Series B, 73(1), 148-159. https://doi.org/10.1093/geronb/gbx019 
  20. Jonsson, A. C., Beach, D., Korp, H., & Erlandson, P. (2012). Teachers' implicit theories of intelligence: Influences from different disciplines and scientific theories. European Journal of Teacher Education, 35(4), 387-400. https://doi.org/10.1080/02619768.2012.662636 
  21. Kim, S. M., & Heo, H. J. (2023). A study on the mathematical beliefs of elementary school teachers with a focus on mathematical mindset. School Mathematics, 25(1), 31-58. https://doi.org/10.57090/sm.2023.03.25.1.31 
  22. Kline, R. B. (2011). Convergence of structural equation modeling and multilevel modeling. In M. Williams, & W. P. Vogt (Eds), The Sage handbook of innovation in social research methods (pp. 562-589). SAGE Publications. https://doi.org/10.4135/9781446268261 
  23. Laine, S., & Tirri, K. (2023). Literature review on teachers' mindsets, growth-oriented practices and why they matter. Frontiers in Education, 8, 1275126. https://doi.org/10.3389/feduc.2023.1275126 
  24. Lee, H. Y., Kim, H. M., Ko, H. K., Park, J. H., Oh, S. J., Lim, M. Y., Tak, B. J., & Hwang, J. H. (2021). A study on ways to improve students' mathematical affective achievement. KOFAC A22040003. 
  25. Lee, S. L., Chan, H. S., Tong, Y. Y., & Chiu, C. Y. (2023). Growth mindset predicts teachers' life satisfaction when they are challenged to innovate their teaching. Journal of Pacific Rim Psychology, 17, 1-11. https://doi.org/10.1177/18344909231167533 
  26. Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767-778. https://doi.org/10.1093/biomet/88.3.767 
  27. Makkonen, T., Lavonen, J., & Tirri, K. (2019). General and physics-specific mindsets about intelligence and giftedness: A study of gifted Finnish upper-secondary-school students and physics teachers. International Journal for Talent Development and Creativity, 7(1), 39-52. 
  28. McLachlan, G. J. (1987). On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Journal of the Royal Statistical Society: Series C (Applied Statistics), 36(3), 318-324. https://doi.org/10.2307/2347790 
  29. Muthen, L., & Muthen, B. (1998). MPlus (version 8.10) [Computer software]. Muthen & Muthen. 
  30. Park, D., Gunderson, E. A., Tsukayama, E., Levine, S. C., & Beilock, S. L. (2016). Young children's motivational frameworks and math achievement: Relation to teacher-reported instructional practices, but not teacher theory of intelligence. Journal of Educational Psychology, 108(3), 300-313. https://doi.org/10.1037/edu0000064 
  31. Patterson, M. M., Kravchenko, N., Chen-Bouck, L., & Kelley, J. A. (2016). General and domain-specific beliefs about intelligence, ability, and effort among preservice and practicing teachers. Teaching and Teacher Education, 59, 180-190. https://doi.org/10.1016/j.tate.2016.06.004 
  32. Rattan, A., Good, C., & Dweck, C. S. (2012). "It's ok-Not everyone can be good at math": Instructors with an entity theory comfort (and demotivate) students. Journal of Experimental Social Psychology, 48(3), 731-737. https://doi.org/10.1016/j.jesp.2011.12.012 
  33. Rissanen, I., Kuusisto, E., Hanhimaki, E., & Tirri, K. (2018). Teachers' implicit meaning systems and their implications for pedagogical thinking and practice: A case study from Finland. Scandinavian Journal of Educational Research, 62(4), 487-500. https://doi.org/10.1080/00313831.2016.1258667 
  34. Ronkainen, R., Kuusisto, E., & Tirri, K. (2019). Growth mindset in teaching: A case study of a Finnish elementary school teacher. International Journal of Learning, Teaching and Educational Research, 18(8), 141-154. https://doi.org/10.26803/ijlter.18.8.9 
  35. Scherer, R., Campos, D. G. (2022). Measuring those who have their minds set: An item-level meta-analysis of the implicit theories of intelligence scale in education. Educational Research Review, 37, 100479. https://doi.org/10.1016/j.edurev.2022.100479 
  36. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. 
  37. Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333-343. https://doi.org/10.1007/BF02294360 
  38. Sun, K. L. (2018). Brief report: The role of mathematics teaching in fostering student growth mindset. Journal for Research in Mathematics Education, 49(3), 330-335. https://doi.org/10.5951/jresematheduc.49.3.0330 
  39. Wang, Q., & Ng, F. F. Y. (2012). Chinese students' implicit theories of intelligence and school performance: Implications for their approach to schoolwork. Personality and Individual Differences, 52(8), 930-935. https://doi.org/10.1016/j.paid.2012.01.024 
  40. Willingham, J. C. (2016). The role of mindset in a mathematics teacher's interpretations and enactments of professional development activities (Publication No. 10146909) [Doctoral dissertation, Middle Tennessee State University]. ProQuest Dissertations Publishing. 
  41. Willingham, J. C., Barlow, A. T., Stephens, D. C., Lischka, A. E., & Hartland, K. S. (2021). Mindset regarding mathematical ability in K-12 teachers. School Science and Mathematics, 121(4), 234-246. https://doi.org/10.1111/ssm.12466 
  42. Yeager, D. S., Carroll, J. M., Buontempo, J., Cimpian, A., Woody, S., Crosnoe, R., Muller, C., Murray, J., Mhatre, P., Kersting, N., Hulleman, C., Kudym, M., Murphy, M., Duckworth, A. L., Walton, G. M., & Dweck, C. S. (2022). Teacher mindsets help explain where a growth-mindset intervention does and doesn't work. Psychological Science, 33(1), 18-32. https://doi.org/10.1177/09567976211028984 
  43. Zhang, J., Kuusisto, E., & Tirri, K. (2020). Same mindset, different pedagogical strategies: A case study comparing Chinese and Finnish teachers. International Journal of Learning, Teaching and Educational Research, 19(2), 248-262. https://doi.org/10.26803/ijlter.19.2.15